# Tag Info

### Reference for anti-commutative Binomial Theorem

In section 3 of Scurlock 2020, expressions are derived for ${{n}\choose{k}}_{-1}$, which relate to this question through the definition $$(x+y)^{n}=\sum_{k=0}^{n}{{n}\choose{k}}_{-1}x^ky^{n-k}$$ ...

### What does "because" mean, in the context of an answer to a mathematical problem?

A true story (just for fun). Once upon a long time ago, the logician Geoffrey Hunter (the author of that excellent old book Metalogic) told me that he used to give a low-level logic course. Near the ...

### Reference or proof for number of permutations of [2n] with longest increasing subsequence of length n.

This can be worked out pretty simply using the Robinson–Schensted correspondence. One of the consequences of this correspondence is that the number of permutations on $m$ letters with longest ...
Accepted

### A reference request for $SL(2,q)$ being quasisimple for prime powers $q\ge 4$.

Here are two possibilities. In Huppert's German book "Endliche Gruppen I", it is proved in Satz (= Theorem) 6.10 on page 181 that ${\rm SL}(n,K)$ is perfect for any field $K$ and $n \ge 2$, ...
Accepted

### What does "because" mean, in the context of an answer to a mathematical problem?

I agree with univalence's comment: "$X$ because $Y$" means, typically, and at least in your examples, that $Y$ is a sketch of a proof of $X$, or perhaps the key step or key theorem that ...
Accepted

### Can an equilibrium be unstable and asymptotically stable at the same time?

No, it cannot. By definition, an equilibrium point is asymptotically stable if it is both stable and attractive. Therefore, if the equilibrium point is unstable, it cannot be asymptotically stable. ...

### Imre Ruzsa Generalisation of Kneser's theorem proof

A proof due to DeVos is found here http://math.colgate.edu/~integers/q7/q7.pdf
Accepted

### Uniqueness of interpolation for distinct positive real numbers by non-negative coefficients $x_i$ and $\sum_{i=1}^n x_i =1$

Write $A = \sum_{i=1}^n a_i x_i$. This expression writes the number $A$ as a convex combination of the distinct positive reals $\{ a_i \}$. The question is equivalent to asking: given that there is at ...
Yes, there are many applications. For instance, it allows you to derive tests to establish the stability of a system for which the matrix $A$ is uncertain (robust analysis). This can be used to ...